Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Abstract

Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

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Cited by in corpus (7)

• Towards adiabatic quantum computing using compressed quantum circuits
• Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks
• Anticoncentration and state design of random tensor networks
• Fermionic Magic Resources of Quantum Many-Body Systems
• Beyond Quantum Annealing: Optimal control solutions to MaxCut problems
• Quantum circuit compilation with quantum computers
• Variational matrix product states for combinatorial optimization